The only thing is that it's not Stannis' men on the boats they're pirates so he probably wont care that much about them. Also Didnt littlefinger promise Renly baratheon that the gates would be open? Cant see why he wouldnt offer the same to Stannis. So I'd say all Stannis bannermen go through the gate, pirates die a firey water death.
also king's landing is at the mouth of a river leading into the sea so it's next to the sea
littlefinger would say anything to anyone he is only loyal to himself, but in the book he was sent to highgarden to get the tyrells to join the lanisters after renlys death, so it's probaly just cutting out a scene for tv to have him there at the death